Key Concepts

• Success in “solving” Rubik’s Cube depends on discovering short se­quences of moves that accomplish limited goals.
• But the strategy is so successful that the authors yearned for puzzles whose solutions would require novel tactics.
• Basing their work on the mathematical theory of groups so well illustrated by Rubik’s Cube, the authors have devised three new games that challenge today’s generation of puzzle lovers with the complexities of “sporadic simple groups.”

Editor's Note: The online puzzles mentioned in the July magazine can be found here.

Millions of people have been perplexed at one time or another by Rubik’s Cube, a fascinating puzzle that took the world by storm in the 1980s. If you somehow missed the puzzle—or the 1980s—the cube is a plastic gizmo that appears to be made up of 27 small cubes, or “cubies,” stacked into a larger cube, three cubies to an edge. Each of the six square faces of the larger cube is colored in one of six eye-catching colors—typically blue, green, orange, red, yellow or white. We said the cube appears to be a stack of cubies, but appearances here are deceptive. An ingenious mechanism, invented in 1974 by a Hungarian teacher named Erno Rubik (and, independently, in 1976 by a Japanese engineer named Terutoshi Ishige), enables any of the six square faces of the large cube to be twisted about the center of that face. Twist the faces in some random sequence five or six times, and you have a cube so scrambled that only an expert—a cubemeister—can restore order. The object of the puzzle is to put an arbitrarily scrambled cube back into its original state, one solid color per face, thereby “solving” the cube.

   
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